Question

which graph matches this table?

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$$\begin{tabular}{|c|c|c|c|} \\hline input (x) & -2 & 0 & 2 \\\\ \\hline output (y) & -1 & 1 & 3 \\\\ \\hline \\end{tabular}$$

Explanation:

Identify the coordinates from the table

$$ (-2, -1), \quad (0, 1), \quad (2, 3) $$

Verify points on each graph option

• Left graph: passes through \((-2, 3)\), \((0, 1)\), \((2, -1)\).
• Middle graph: passes through \((-2, -1)\), \((0, 1)\), \((2, 3)\).
• Right graph: passes through \((-2, -2)\), \((0, 0)\), \((2, 2)\).

Determine the matching graph

$$ \text{Middle graph matches } (-2, -1), (0, 1), (2, 3) $$

Answer:

• (A) Left graph: line passing through \((-2, 3)\), \((0, 1)\), and \((2, -1)\)
• (B) Middle graph: line passing through \((-2, -1)\), \((0, 1)\), and \((2, 3)\) (Correct answer)
• (C) Right graph: line passing through \((-2, -2)\), \((0, 0)\), and \((2, 2)\)